Lots of places outside the US have co-ed bathroom facilities -- as in you walk in the door, and the guys are standing at the urinal (with a room divider) when you walk in. (never freaked me out, other than a momentary "oh, I've walked in the wrong door")

Most public toilets outside the US have unisex handwash facilities.

am guessing most adult men have seen a woman apply lipstick, wash her hands, or brush her hair.

Certainly very common in Spain for their to be only a single toilet in small bars and the like. That doesnt bother me. However, for reasons I can't really explain, the increasing trend for there to be uni-sex toilet facilities, with several adjacent cubicles, does bother me somewhat. Dunno why, I just feel uncomfortable - no doubt it's a generation thing

It has been a growing trend because people who design and/or operate public spaces, including bar owners and restaurateurs find it more efficient to comply with absurd local building ordinances / judicial interpretations of the equal rights amendment by having co-ed sinks or completely co-ed bathrooms. The difference between equal floor space and equal access to facilities.

It solves two problems, one being the over-allocation of space to bathrooms. e.g. if you only needed 6 toilet/urinal facilities between men and women, 1 being handicapped sized and 2 being urinals, the rest being regular sized toilets, but have to set aside space for two bathrooms, one with 4 toilets for the women, one being handicapped sized and one with 2 toilets, one being handicapped sized and two urinals.)

The second problem of inefficient allocation of space it solves is where you can often find the toilets in the Men's room unused while there is a long line for the Ladies' facilities.

There is a social problem, because some people like you prefer to not co-mingle between sexes in bathrooms. It's not just a social "ick" factor, bathrooms have also socially evolved to be used by both men and women as a "refuge" from each other, or to congregate, and sometimes to talk about each other.

I was amazed when first I discovered that some of the nicer women's restrooms had comfy sofas and live flower arrangements. Whereas the 'nicer' men's restrooms simply didn't keep the roll of TP on the floor tile beside the toilet...

There's an old and storied men's club in Philadelphia whose ladies rooms not only have flowers, but each stall has its own upholsterd bench to lie down on. Of course, these were built for the Victorian women who only entered the club on great occasions like balls.

One of my regular road trip pit stops has lovely decorations in the women's restroom. The gas stations is a little run down, as rural gas stations tend to be, but the women's restroom is clean and they have decorative art and even an artificial ficus. One day I stopped by and the women's room was occupied. The occupant was taking a long time, and the men's room was vacant, so I went for it. Big mistake. Stinky, dirty, and no art!